Brahim Belhaouari, samir and Mountford, Thomas (2006) Convergence results and sharp estimates for the voter model interfaces. E l e c t r o n i c J o u r n a l o f P r o b a b i l i t y (30). pp. 768-801. ISSN ELECTRONIC JOURNAL OF PROBABILITY
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Abstract
We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite th moment for some gamma > 3, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scaling. This extends recent work of Newman, Ravishankar and Sun. Our result is optimal in the sense that finite th moment is necessary for this convergence for all gamma in (0, 3). We also obtain relatively sharp estimates for the tail distribution of the size of the equilibrium interface, extending earlier results of Cox and Durrett, and Belhaouari, Mountford and Valle
| Item Type: | Article |
|---|---|
| Impact Factor: | 0.7 |
| Subjects: | R Medicine > RZ Other systems of medicine Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| ID Code: | 2717 |
| Deposited By: | Dr Samir Brahim Belhaouari |
| Deposited On: | 21 Sep 2010 00:37 |
| Last Modified: | 19 Jan 2017 08:27 |
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Convergence results and sharp estimates for the
voter model interfaces. (deposited 02 Apr 2010 02:13)
- Convergence results and sharp estimates for the voter model interfaces. (deposited 16 Mar 2011 06:10)
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- Convergence results and sharp estimates for the voter model interfaces. (deposited 18 Aug 2010 08:38)
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